Tessellation, shamanism, and being alive to things

This study examines the entanglement of affects that occurred during a short episode at a science museum. The episode involved a small number of children and a teacher who had come to the museum in the context of a school field trip. It took place inside an exhibit called ‘Hmong House’, which reproduced various components of a traditional house of the Hmong people. A key aim of this paper is to trace, via the microethnographic analysis of a brief video recording, an affective journey meshing mathematical tessellation and Hmong shamanism. In addition, we elaborate on ways in which disparate themes, such as tessellation and shamanism, became interwoven in the life of those visiting the Hmong House at the time. The episode of the Hmong House may inspire other activities in which students or visitors, with life trajectories partially rooted in Indigenous cultures, can share practices that are foreign to other students. The most important qualities of these activities, we suggest, are the respectful dignity with which they are demonstrated and engaged with, and the freedom to undertake interdisciplinary journeys–without subjection to artificial disciplinary boundaries–in which improvisation and surprising turns are expected and ever-present

Desarrollo del concepto de diferencia algebraica a través del movimiento

En este trabajo presentamos un estudio de casos con niños de 11 años para explorar el concepto de diferencia algebraica. Este estudio forma parte de un trabajo más amplio realizado en el proyecto “Maths and Motion” en la Manchester Metropolitan University (UK), con el objetivo de incrementar nuestra comprensión sobre cómo los estudiantes usan las nuevas tecnologías para dar sentido a conceptos matemáticos. En trabajos previos se ha diseñado un software que permite la exploración de varios conceptos matemáticos a través del uso de sensores de movimiento basados en la tecnología de Nintendo Wii, esta tecnología nos permite registrar los movimientos de los participantes. De acuerdo con numerosos autores (Arzarello, Paola, Robutti, & Sabena, 2009; Elia, Gagatsis, & van den Heuvel-Panhuizen, 2014; Nemirovsky & Ferrara, 2009; Nemirovsky, Rasmussen, Sweeney, & Wawro, 2012) consideramos que el conocimiento matemático está corporeizado, en el sentido de que el movimiento del cuerpo juega un papel central. Esta idea está sustentada en una serie de hallazgos empíricos que relacionan cuerpo, conceptos y cognición en un amplio rango de disciplinas

Literacy and emancipation: on the work and thought of Myriam Nemirovsky (Alfabetizar y emancipar: sobre el trabajo y el pensamiento de Myriam Nemirovsky)

This article reviews contributions to teaching reading and writing of Myriam Nemirovsky, whose conceptualization foreshadowed an emancipatory pedagogy. To do so, we have reviewed her work and interviewed three of her colleagues: Elena Laiz Sasiain, Liliana Tolchinsky Brenman and Francesco Tonucci. In the first part we recount key moments in Nemirovsky’s life and set forth ideas that helped her to develop her approaches to teaching reading and writing. The text explores the development of her pedagogical thinking based on her teaching and research experiences. Later, we present parallels between Myriam Nemirovsky’s work and ideas of Jaques Rancière and Joseph Jacotot to highlight core elements in an emancipatory pedagogy and illustrate their presence in Myriam Nemirovsky’s practices and thinking. To conclude, we reflect on how Nemirovsky’s teachings helped to mobilize innovative ideas among educators. Her legacy includes a conception in which learning how to read and write is a contextualized process already underway, always unfinished, in constant transformation and largely unpredictable. It is a vision which no longer prioritizes the measurable, neutral and standardizable

Aesthetical Entanglements in Mathematics Learning

In this paper we develop a perspective on the diverse aesthetics historically associated with mathematics, inspired by Rancière’s approach to aesthetics and politics. We call ‘Silencing Aesthetics’ a dominant aesthetic that Rota has characterized as a “copout (...) intended to keep our formal description of mathematics as close as possible to the description of a mechanism.” The challenge this paper attempts to explore is how to question silencing aesthetics to make space for generative ones. Our efforts have focused on setting up and studying inclusive and pluralist ‘Studios’, gathering craftworkers, anthropologists, mathematics educators and mathematics enthusiasts. We include here a case study based on a conversation among basket weavers, anthropologists, and mathematics educators, focused on the artisanal and mathematical nature of knots

Crafts and the Origins of Geometry

In this paper, we explore the possible roles of craftwork at the origins of geometry. Since shapes are the characters of geometry, our focus is on crafting shapes. We review two approaches to the nature of making: hylomorphism and hylonoesis. Related to these, we distinguish between ‘shape’ and ‘shaping’. From studies on prehistoric pottery, we explore a conception of ‘shaping’ as thoroughly implicated by the manifold social, biological, and material life of a community. Then we explore the significance of ’shaping’, which animate shapes, immerse them in the vagaries of materiality, and fill them with secrets longing for their open realization; a realization that is at once — inseparably — material and imaginary. We make shapes as they shape our bodies, and then we become capable of imagining and gesturing them

Aesthetical entanglements in mathematics education

In this study, we develop a perspective on the diverse aesthetics historically associated with mathematics, inspired by Rancière's approach to aesthetics and politics. We call “Silencing Aesthetics” a dominant aesthetic that Rota has characterized as a “copout (…) intended to keep our formal description of mathematics as close as possible to the description of a mechanism”. The challenge this study attempts to explore is how to question silencing aesthetics to make space for inclusive ones. Our efforts have focused on setting up and studying inclusive and pluralist “Studios”, gathering craftworkers, anthropologists, mathematics educators, and mathematics enthusiasts. We include here a case study based on a conversation amongst basket weavers, anthropologists, and mathematics educators focused on the artisanal and mathematical nature of knots. We discuss the implications of aesthetical entanglements, such as those in our case study, for mathematics learning

Owning and Reflecting: On the Creation of a Teacher-Research Group

he inadequacy of such an approach emulating medical research stems from the fact that in education there are no well defined equivalents of "illness" and "treatment." No isolated aspect of an educational practice can be an independent causal factor. Any tool, text, curricular sequence, demonstration, classroom arrangement, can play out in extraordinarily diverse ways depending on how is becomes part of the culture, purposes, and life of students and teachers. Therefore, any significant conclusion that we draw has to be embedded in the complex background and specific events lived by the participants in an educational episode. A teacher-research group aims at reflecting on educational episodes without losing touch with the manifold stories and contexts of life as experienced by students and teachers. In our own view, we see educational theorizing not as the development of abstract models to describe hidden cognitive and social mechanisms, but ways of being in, relating to, and bringing

Children creating ways to represent changing situations: on the development of homogeneous spaces

This paper focuses on children creating representations on paper for situations that change over time.We articulate the distinction between homogeneous and heterogeneous spaces and reflect on children’s tendency to create hybrids between them. Through classroom and interview examples we discuss two families of tasks that seem to facilitate children’s development of homogeneous spaces: 1) making selected features directly visible, instead of requiring intermediate steps and calculations; for example, to be able to directly compare different sets of data combined in a single graph, and 2) exploring well-defined figural components that can be used in graphing, such as line segments or sequencing from left to right, that are introduced as a resource